Pythagorean Theorem and Its Converse Pythagorean Theorem If

Pythagorean Theorem and Its Converse

Pythagorean Theorem – If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Finding the Length of the Hypotenuse • c = 29

Simplest Radical Form 2. Simplify 20 or 2 10 2 5

Simplest Radical Form 3. Simplify or 192 2 96 2 48 6 8 2 32 4 2 2

Finding the Length of the Leg 4. What is the value of x? Express your answer in simplest radical form.

Converse of the Pythagorean Theorem • If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.

Pythagorean Triples A Pythagorean triple is a set of nonzero whole numbers, a, b, and c that always satisfy the equation a² + b² = c². Some common Pythagorean Triples: 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25 Keep an eye out for the multiples of these common Pythagorean Triples (ex. 6, 8, 10)

Obtuse and Acute Triangles • If the square of the length of the longest side of a triangle is GREATER THAN the sum of the squares of the lengths of the other two sides, then the triangle is OBTUSE. • If the square of the length of the longest side of a triangle is LESS THAN the sum of the squares of the lengths of the other two sides, then the triangle is ACUTE.

Classifying a Triangle 5. A triangle has side lengths 6, 11, and 14. Is it acute, obtuse, or right? c² ___ a² + b² 14² ___ 6² + 11² 196 ___ 36 + 121 196 ___ > 157 The triangle is obtuse.

Homework • Worksheet: The Pythagorean Theorem and Its Converse #’s 1 -18